To begin with, let us present the relevant thermodynamic quantities in the EPS formalism.
First, the total energy \(E\)  of the black hole spacetime, as calculated using
the Noether charge associated with the
timelike Killing vector [1]}, reads
\(E&=\frac{\alpha \omega _2}{24\pi }\left[\frac{(c_0-\epsilon )(\Lambda r_0^2-3c_0)}{3 r_0}+\frac{(2\Lambda r_0^2-c_0+\epsilon )d}{r_0^2}\right],\) 
